>  I am desperately looking for a scene-wide collections of materials, but I can't find it.

You want scene-wide materials?:

    >>> bpy.data.materials[:]
    [bpy.data.materials['Material'], bpy.data.materials['Material.001']]

this shows the materials for one object:

    >>> bpy.data.objects['Circle'].material_slots[:]
    [bpy.data.objects['Circle'].material_slots[0], bpy.data.objects['Circle'].material_slots[1]]

or

    >>> [m.name for m in bpy.data.objects['Circle'].material_slots[:]]
    ['Material.001', 'Material.002']


_______________________________

For completeness then

### bpy.data.materials indices

For sake of argument I have a scene with 4 materials

	>>> bpy.data.materials[:]
	[bpy.data.materials['MAT A'], bpy.data.materials['MAT B'], bpy.data.materials['MAT C'], bpy.data.materials['MAT D']]

There's no helper function that I'm aware of that will convert the name of the material to its index (in the materials collection), there's no need to because we can use the name (a string) directly to get the reference.

	>>> my_material = bpy.data.materials['MAT D']
	>>> my_material.name
	'MAT D'

While we can do a lookup by index like this

	>>> bpy.data.materials[0]
	bpy.data.materials['MAT A']

If you really wanted to find the index of 'MAT A' in `.data.materials`, you could do a `.find()` because material names are allways unique .

	>>> bpy.data.materials.find('MAT A')
	0

### material slot indices

The material slot indices refer to the order in which your materials appear in the object's 'material stack'. 

![IMAGE][1]

	>>> obj = bpy.data.objects['Icosphere']
	>>> obj.material_slots[:]
	[bpy.data.objects['Icosphere'].material_slots[0], bpy.data.objects['Icosphere'].material_slots[1]]

If you want a direct reference to the material in a slot, boom. its easy too.

	>>> obj.material_slots[:][0].material
	bpy.data.materials['MAT A']

No need to get the name first.

	>>> obj.material_slots[:][0].name
	'MAT A'

If the material_slot_index is 1, and I have two materials referenced by the object (MAT D and MAT C), then 1 refers to MAT C and globally MAT C is index 2. I may be a point of some confusion that the term index is used to talk about the location of an item in two different types of collections.


  [1]: https://i.sstatic.net/94Zss.png